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Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
We present three algorithms to reduce homogeneous linear differential equations to their simplest form. Factoring a differential operator reduces a differential equation L(y)=0 to equations of minimal order, but this is not the only...
To solve globally bounded order $3$ linear differential equations with rational function coefficients, this thesis introduces a partial $_3F_2$-solver (Section~\ref{3F2 type solution}) and $F_1$-solver (Chapter~\ref{F1 solver}), where $...
We show that path components of central extensions of a simplicial group $G$ by a simplicial abelian group $A$ are in bijection with the homotopy classes of maps between classifying spaces $[\overline{W}G, \overline{W}^2A]$. Generalizing...
We study functional data defined by an underlying structure (modeled as a metric space or ametric measure space) and feature information (represented by a 1-Lipschitz function on the ground structure). If the ground structure is a metric...
In this thesis we develop a few algorithms that are useful for factoring linear recurrence operators. We approach the factorization problem from three directions. First, considering reduction modulo a prime leads to the study of...
This thesis introduces two new algorithms to find hypergeometric solutions of second order regular singular differential operators with rational function or polynomial coefficients. Algorithm 3.2.1 searches for solutions of type: exp(∫ r...
It is known that the category of Waldhausen categories is a closed symmetric multicategory and algebraic K-theory is a multifunctor from the category of Waldhuasen categories to the category of spectra. By assigning to any Waldhausen...
The Weisfeiler-Leman algorithm is a powerful test of graph isomorphism, and works by iteratively isolating clusters of nodes via a coloring scheme based on binary relationships. This refinement process is akin to message passing on graph...
This thesis has two parts. The first part concerns topological invariants of the n-gonal plane curves. Our first result is an application of Krammer representations to the Libgober invariant for plane curve complements. This gives a...
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